Yea, but WWE owns all that shit (WCW, ECW) so they don't distinguish it really unless necessary. If you watch the list on Netflix, they show footage from all three companies and acknowledge multiple names for the same finisher (ex: Chris Jericho - Lion Tamer / Walls of Jericho)

Gotta give Mankind props for the Mandible Claw / Socko. I never thought about it at the time, but its dope how he turned it from a heel finisher to a face finisher. Cant think of anyone who ever really did that.